I don't live in the SE but have in the past. I know how fast grass grows there and I would certainly consider haying it rather than mowing it. When I moved here, I had the same idea. I have hired it cut, but in my area it is difficult, and sometimes expensive. I bought haying equipment and do it myself. If the equipment is in good condition and is the right equipment, it's a pleasant enough thing to do. But those a pretty big "if's". With all of the aggravation, and problems, if I had 10 to 20 acres of grass growing land in Georgia, I'd try it. Haying the land keeps it nice and in good condition. It may take a little time to get everything working smoothly, but it's worth it imo. A lot of very small acreages (one acre and two acres) here are hayed by contract hay guys. The thing is that you will need to cut the grass and keep the land in good condition one way or another. After all these years, I still think the way to do that is by haying it - and if you can get a good farmer to do it, it's a great solution. In the areas of the SE with which I am familiar, it is not difficult to get someone to cut and bale hay on small acreages.
Not in GA anymore, but that's a very common arrangement up here. I know several people with small farmettes who lease out portions to farmers to grow hay. Mostly I think they don't charge anything, it allows them to characterize the property as agriculture for tax purposes and avoids the need for the owner to mow/maintain the land.
One word of caution is to make sure you specify what can be grown. A friend had a lovely field and the farmer they leased it to grew fescue without notifying them first. The fescue "crept" into some of the fields they used for turnout after it had been planted in the haying area. Now they have a lot of fescue around and it's exactly what they DIDN'T want and they're going to have to spend their own $$$ to get rid of it once the lease is up. So just add that to the list of things to think about if you breed or have specific needs for the property that could be affected by what hay is being grown.
I have 10 acres that were formerly in tobacco. Mostly to maintain the ag tax exemption, I'm growing orchard grass hay on it. I use the hay for my horses and sell the surplus. There is NO profit in it. It was less money to buy the hay than the inputs for an equal amount of hay. I do have very premium hay. Harvested for quality rather than number of bales. To get that quality, timing is everything. But no one wants to leave their own fields to work my 10 acres at the peak hay time & weather. So I had to buy the equipment.
Just to get out of mowing, first contact any neighboring hay operations. The closer, the more likely they would be willing to take your land on. Moving equipment is a major effort and time waster.
hosspuller brings up a good point. The last time I tried to get someone else to cut my hay, he didn't contact me to actually do it until way after the best time to cut it. Fortunately, I just went out and did it and didn't wait for him. When he finally called to come, I found out that he had been cutting a bunch of 1 and 2 acre properties rather than my 40 acre field. I didn't understand it, but haven't called anytone since. Like I said, I like to do it if I have time and nothing breaks. It's certainly not cheaper.
Here people often do a split of the hay for the cutting. Landowner keeps some, conractor gets some - the percentage just depends.
We have a hay field, about a mile from the house and other pastures, that I tried raising hay on 25 years ago. We have the wrong micro-climate for horse hay, so I sold the equipment, and have since then just let someone else grow, and bale cow hay on it. He got old enough to quit working so much, so he cut back on his herd, and stopped using our field.
Now I'm back to cutting it myself. It's not so bad with a big mower. This fall when I was cutting it, a Red-Tailed Hawk caught four field rats while I was mowing, with one maybe 40 feet away at most.
There is no one else close enough who would be interested in growing cow hay, so it's another job for me now. I might plant it in pine trees.